An approach based on the pseudospectral method for fractional telegraph equations

Haifa Bin Jebreen; Beatriz Hernández-Jiménez; Haifa Bin Jebreen; Beatriz Hernández-Jiménez

doi:10.3934/math.20231496

AIMS Mathematics

2023, Volume 8, Issue 12: 29221-29238. doi: 10.3934/math.20231496

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An approach based on the pseudospectral method for fractional telegraph equations

Haifa Bin Jebreen ^{1
,
,},
Beatriz Hernández-Jiménez ²

1.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
Departamento de Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, 41013 Sevilla, Spain

Received: 16 August 2023 Revised: 08 October 2023 Accepted: 12 October 2023 Published: 26 October 2023
MSC : 54A25, 65M70, 65Bxx, 35L20

We aim to implement the pseudospectral method on fractional Telegraph equation. To implement this method, Chebyshev cardinal functions (CCFs) are considered bases. Introducing a matrix representation of the Caputo fractional derivative (CFD) via an indirect method and applying it via the pseudospectral method helps to reduce the desired problem to a system of algebraic equations. The proposed method is an effective and accurate numerical method such that its implementation is easy. Some examples are provided to confirm convergence analysis, effectiveness and accuracy.
- convergence analysis,
- Chebyshev cardinal functions,
- fractional Telegraph equation,
- pseudospectral method
Citation: Haifa Bin Jebreen, Beatriz Hernández-Jiménez. An approach based on the pseudospectral method for fractional telegraph equations[J]. AIMS Mathematics, 2023, 8(12): 29221-29238. doi: 10.3934/math.20231496

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Abstract

We aim to implement the pseudospectral method on fractional Telegraph equation. To implement this method, Chebyshev cardinal functions (CCFs) are considered bases. Introducing a matrix representation of the Caputo fractional derivative (CFD) via an indirect method and applying it via the pseudospectral method helps to reduce the desired problem to a system of algebraic equations. The proposed method is an effective and accurate numerical method such that its implementation is easy. Some examples are provided to confirm convergence analysis, effectiveness and accuracy.

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